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Math Help - Integration help

  1. #1
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    Integration help

    \int sec^45x dx
    =\int (sec^25x)(sec^25x) dx
    =\int (1+tan^25x)sec^25x dx
    =\int (sec^25x + tan^25xsec^25x)dx
    =\int sec^25x dx + \int tan^25xsec^25x dx
    =\frac{1}{5}tan5x + ??????

    I don't know what to do with the second integral, or if I am even starting this problem the right way. I have the solution, but it is missing all of the steps past the trig identity. TIA.
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  2. #2
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    Re: Integration help

    Quote Originally Posted by wondering View Post
    \int sec^45x dx
    =\int (sec^25x)(sec^25x) dx
    =\int (1+tan^25x)sec^25x dx
    =\int (sec^25x + tan^25xsec^25x)dx
    =\int sec^25x dx + \int tan^25xsec^25x dx
    =\frac{1}{5}tan5x + ??????
    =\int sec^25x dx + \int tan^25xsec^25x dx
    =\frac{1}{5}tan5x + \frac{1}{15}\tan^3(5x)+C
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  3. #3
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    Re: Integration help

    Thanks Plato. Is it just a simple u substitution that I am not seeing? Can you explain the second integral in steps for me. Thanks for your help.
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  4. #4
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    Re: Integration help

    Never mind I see it now. Thanks for the help, I was having a mental block for a moment there.
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